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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 303 · 40 questions
TalentJR

How to do it in your head (Guess, divide, average): Division: round the divisor to the nearest ten and find the closest multiple of it. Square root: guess the nearest whole root, then divide the number by your guess. Average the guess and the answer of the division, and round to 1 decimal place.

NameDateTime takenScore ___ / 40
  1. 1.√31 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.7 (d) 5.6
  2. 2.√69 to 1 decimal place? (a) 8.6 (b) 8.3 (c) 8.5 (d) 8.4
  3. 3.Best estimate of 1837 ÷ 26? (a) 6100 (b) 610 (c) 61
  4. 4.√41 to 1 decimal place? (a) 6.3 (b) 6.1 (c) 6.4 (d) 6.2
  5. 5.Best estimate of 4513 ÷ 72? (a) 64 (b) 640 (c) 6400
  6. 6.√43 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.3 (d) 6.4
  7. 7.Best estimate of 7568 ÷ 83? (a) 9500 (b) 950 (c) 95
  8. 8.Best estimate of 3401 ÷ 47? (a) 68 (b) 680 (c) 6800
  9. 9.Best estimate of 3663 ÷ 57? (a) 610 (b) 6100 (c) 61
  10. 10.Best estimate of 1432 ÷ 56? (a) 24 (b) 2400 (c) 240
  11. 11.Best estimate of 2077 ÷ 28? (a) 690 (b) 6900 (c) 69
  12. 12.√92 to 1 decimal place? (a) 9.7 (b) 9.9 (c) 9.8 (d) 9.6
  13. 13.√37 to 1 decimal place? (a) 6.3 (b) 6.2 (c) 6.0 (d) 6.1
  14. 14.√75 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 8.7 (d) 9.0
  15. 15.Best estimate of 4372 ÷ 56? (a) 73 (b) 730 (c) 7300
  16. 16.Best estimate of 926 ÷ 76? (a) 12 (b) 120 (c) 1200
  17. 17.Best estimate of 769 ÷ 37? (a) 190 (b) 1900 (c) 19
  18. 18.Best estimate of 7272 ÷ 76? (a) 9100 (b) 910 (c) 91
  19. 19.Best estimate of 5495 ÷ 59? (a) 92 (b) 9200 (c) 920
  20. 20.Best estimate of 951 ÷ 56? (a) 160 (b) 1600 (c) 16
  21. 21.√84 to 1 decimal place? (a) 9.1 (b) 9.3 (c) 9.0 (d) 9.2
  22. 22.Best estimate of 944 ÷ 42? (a) 2400 (b) 24 (c) 240
  23. 23.Best estimate of 1251 ÷ 42? (a) 3100 (b) 31 (c) 310
  24. 24.√77 to 1 decimal place? (a) 9.1 (b) 8.8 (c) 8.9 (d) 9.0
  25. 25.Best estimate of 6559 ÷ 86? (a) 730 (b) 73 (c) 7300
  26. 26.Best estimate of 1305 ÷ 36? (a) 330 (b) 33 (c) 3300
  27. 27.√61 to 1 decimal place? (a) 7.7 (b) 7.8 (c) 7.6 (d) 7.9
  28. 28.√66 to 1 decimal place? (a) 8.1 (b) 8.0 (c) 8.2 (d) 8.3
  29. 29.Best estimate of 1513 ÷ 29? (a) 50 (b) 5000 (c) 500
  30. 30.Best estimate of 4411 ÷ 66? (a) 6300 (b) 630 (c) 63
  31. 31.Best estimate of 7267 ÷ 82? (a) 910 (b) 91 (c) 9100
  32. 32.Best estimate of 652 ÷ 23? (a) 3300 (b) 33 (c) 330
  33. 33.√62 to 1 decimal place? (a) 7.9 (b) 7.6 (c) 7.7 (d) 7.8
  34. 34.Best estimate of 1560 ÷ 73? (a) 220 (b) 22 (c) 2200
  35. 35.Best estimate of 6820 ÷ 72? (a) 970 (b) 9700 (c) 97
  36. 36.Best estimate of 5492 ÷ 63? (a) 9200 (b) 920 (c) 92
  37. 37.√63 to 1 decimal place? (a) 7.8 (b) 8.1 (c) 8.0 (d) 7.9
  38. 38.Best estimate of 1592 ÷ 22? (a) 800 (b) 8000 (c) 80
  39. 39.√59 to 1 decimal place? (a) 7.6 (b) 7.7 (c) 7.9 (d) 7.8
  40. 40.Best estimate of 2438 ÷ 26? (a) 810 (b) 8100 (c) 81

Answer key

  1. 5.6
  2. 8.3
  3. 61
  4. 6.4
  5. 64
  6. 6.6
  7. 95
  8. 68
  9. 61
  10. 24
  11. 69
  12. 9.6
  13. 6.1
  14. 8.7
  15. 73
  16. 12
  17. 19
  18. 91
  19. 92
  20. 16
  21. 9.2
  22. 24
  23. 31
  24. 8.8
  25. 73
  26. 33
  27. 7.8
  28. 8.1
  29. 50
  30. 63
  31. 91
  32. 33
  33. 7.9
  34. 22
  35. 97
  36. 92
  37. 7.9
  38. 80
  39. 7.7
  40. 81

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